Bark scale

The Bark scale is a psychoacoustical scale proposed by Eberhard Zwicker in 1961. It is named after Heinrich Barkhausen who proposed the first subjective measurements of loudness.

The scale ranges from 1 to 24 and corresponds to the first 24 critical bands of hearing. The subsequent band edges are (in Hz) 20, 100, 200, 300, 400, 510, 630, 770, 920, 1080, 1270, 1480, 1720, 2000, 2320, 2700, 3150, 3700, 4400, 5300, 6400, 7700, 9500, 12000, 15500; the centers are 50, 150, 250, 350, 450, 570, 700, 840, 1000, 1170, 1370, 1600, 1850, 2150, 2500, 2900, 3400, 4000, 4800, 5800, 7000, 8500, 10500, 13500.

It is related to, but somewhat less popular than the mel scale.

To convert a frequency f (Hz) into Bark use:

$\text{Bark} = 13 \arctan(0.00076f) + 3.5 \arctan((f/7500)^2) \,$

or (traunmuller 1990)

$\text{Critical band rate (bark)} = [(26.81 f) / (1960 + f )] - 0.53 \,$

if result < 2 add 0.15*(2-result)
if result > 20.1 add 0.22*(result-20.1)

$\text{Critical bandwidth (Hz)} = 52548 / (z^2 - 52.56 z + 690.39) \,$ with z in bark.

OR f = 600*sinh(z/6)

See also

• Luminosity function, which describes the average sensitivity of the human eye to light of different wavelengths.
• Fletcher–Munson curves

External links

• Smith and Abel - Bark and ERB Bilinear Transforms (1999)
• Auditory scales of frequency representation